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In derivation of quadrupole effect (which influences NMR spectrum for nuclei with spin ≥ 1/2), there is one step I do not understand, it is Eckart Wiegner theorem, more specific:

just relavant equations:

Q_{αβ}=∫(3x_{α}x_{β}-δ_{αβ}r^{2})ρdr

So here is the W-E:

<I,m|Q_{αβ}|I,m'>=C<I,m|3/2(I_{α}I_{β}-I_{β}I_{α})-δ_{αβ}I^{2}|I,m'>

and we expres constant C witm matrix element for m=m'=I, and α=β=z:

eQ=<I,I|Q_{zz}I,I|>=C<I,I|3I_{z}^{2}-I^{2}|I,I>=<I,I|I(2I-1)|I,I>

questions:

how can we express Q_{αβ}with spin operator?

can someone comment on every step what is being done? I would like to understand this intuitively if possible...Great thanks!

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# Wiegner Eckart theorem, I don't understand it!

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